Course syllabus for Introductory course in mathematics

The course syllabus contains changes
See changes

Course syllabus adopted 2019-02-21 by Head of Programme (or corresponding).

Overview

  • Swedish nameInledande matematik
  • CodeMVE012
  • Credits7.5 Credits
  • OwnerTKIEK
  • Education cycleFirst-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 51118
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0114 Laboratory 1.5 c
Grading: UG		1.5 c
0214 Examination 6 c
Grading: TH		6 c
  • 28 Okt 2020 am J
  • 07 Jan 2021 pm J
  • 19 Aug 2021 am J

In programmes

Examiner

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Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Aim

The purpose of the course is to strengthen, deepen and develop the knowledge in secondary school mathematics and to thereby give a solid ground for further studies in mathematics.

Learning outcomes (after completion of the course the student should be able to)

After completed course the students shall

- know the elementary functions, what computational rules applies to them, how they relate, how their graphs can be constructed and be able to use this in solving problems of a fairly complex nature and basic modelling

- understand, be able to define, determine and use various basic properties of real valued functions of one real variable, such as domain/range, increasing/decreasing, even/odd, asymptotes and invertibility.

-  understand and be able to define various types of limits of real valued functions of one real variable, know the basic theorems that applies to them and with judgement be able to use these when solving problems.

- understand and be able to define the concept of a continuous real valued function of one real variable, know the basic theorems that applies to them and use these when solving problems. 

- understand and be able to define the concepts of differentiable real valued function of one real variable and the derivative of such a function, know and be able to prove basic theorems that applies to them and with judgement use these when solving problems.

- be able to solve systems of linear equations with several rows and variables using row operations to echelon form and be able to determine the number of solutions to such systems.

- understand and be able to use the complex numbers and the complex exponential function when solving problems.

- be able to use basic concept with respect to linear analytical geometry in three dimensions to determine equations for planes and lines, the distance between such object and area of parallelograms and volume of prallelepipeds.

- be able to use the software MATLAB to handle row/column vectors, matrices and systems of linear equations, plot graphs of functions, numerically differentiate them, determine their zeros and with support illustrate planes and lines in space and write basic programs in m-files using For, While and If statements.

Content

Elementary functions and their properties.
- Basic theory of functions.
- Limits, continuity and derivative of real valued functions of one real variable and how these concepts relate.
- Linearization of a function and tangent line and normal to a plane curve.
- Construction of graphs.
- Modelling and optimization of basic nature.
- Handling undetermined expressions in limits.
- Complex numbers and the complex exponential function.
- Systems of linear equations and row operations.
- Linear analytic geometry in three dimensions.
- Basic use of the software MATLAB.

Organisation

Instruction is given in lectures, classes and during laboratory sessions. More detailed information will be given on the course web page before start of the course.

Literature

Literature will be announced on the course web page before start of the course.

Examination including compulsory elements

More detailed information about the examination will be given on the course web page before start of the course.
Examples of assessments are:
- selected exercises are to be presented to the teacher orally or in writing during the course,
- optional assessments during the course that can result in bonus points,
- project work, individually or in group,
- written exam at the end of the course.
- solving exercises using software which are assessed at the computer.

The course syllabus contains changes

  • Changes to examination:
    • 2020-09-30: Grade raising No longer grade raising by GRULG
    • 2020-07-09: Examination date Examination date changed from 2021-08-25 to 2021-08-19 by Elisabeth Eriksson
      [2021-08-25 6,0 hec, 0214]
    • 2020-07-09: Examination date Examination date changed from 2021-01-05 to 2021-01-07 by Elisabet Eriksson
      [2021-01-05 6,0 hec, 0214]